This invention relates to the compensation of chromatic dispersion, hereinafter referred to as dispersion, in optical transmission systems.
Linear (first order) dispersion, D, is the measure of the rate of change of group delay, xcfx84, with wavelength, xcex. (D=dxcfx84/dxcex.) Linear dispersion is typically measured in picoseconds per nanometre (ps/nm). In the case of a transmission medium, for instance an optical fibre waveguide, whose waveguiding properties are uniform along its length, the linear dispersion exhibited by the medium is proportional to its length and so, for such a medium, it is convenient to define its linear dispersion per unit length, also known as its linear dispersion power. This is typically measured in picoseconds per nanometre per kilometre (ps/nm/km).
The value of the linear dispersion of a transmission path is generally itself a function of wavelength, and so there is a quadratic (second order) dispersion term, Q, also known as dispersion slope, which is a measure of the rate of change of linear dispersion with wavelength. (Q=dD/dxcex=d2xcfx84/dxcex2.) This is typically measured in picoseconds per nanometre squared (ps/nm2). In some, but not all instances, the effects of quadratic dispersion in NDS and DC fibre (non dispersion shifted fibre, and dispersion compensating fibre) are small enough not to assume significance. There are also higher dispersion terms, whose effects generally assume even less significance.
In a digital transmission system the presence of dispersion leads to pulse broadening, and hence to a curtailment of system reach before some form of pulse regeneration becomes necessary. The problem presented by dispersion increases rapidly with increasing bit rate. This is because, on the one hand, increasing the bit rate produces increased spectral broadening of the pulses, and hence increased dispersion mediated pulse broadening; while on the other hand, increasing the bit rate also produces a reduction in the time interval between consecutive bits. In a WDM (wavelength division multiplexed) digital transmission system, it is not practical to minimise the problems of dispersion by choosing to employ a transmission medium exhibiting near-zero first order dispersive power because low first order dispersive power is associated with aggravated non-linear (e.g. four-wave mixing) distortion. A known solution to this problem is to employ xe2x80x98managed dispersionxe2x80x99 in which near-zero aggregate linear dispersion over a particular transmission path is achieved by the use of alternating sections respectively exhibiting positive linear dispersion and negative linear dispersion, for instance by the use of NDS and DC optical fibre waveguide.
Having regard to the manufacturing tolerances in practice encountered in the fabrication of NDS and DC fibre, achieving adequately low aggregate linear dispersion becomes increasingly difficult as the bit rate is increased. Consider for instance a 40 Gbit/s WDM transmission system with a reach of 400 km, and with the shortest and longest wavelength channels separated by 200 nm. The actual amount of linear dispersion in any particular channel that can be tolerated will of course be dependent upon a number of system parameters, but typically may lie in the region of 100 ps/nm. A typical NDS fibre exhibits, at a wavelength of 1550 nm, a linear dispersive power of approximately 17 ps/(nmxc2x7km), and a quadratic dispersive power of approximately 0.058 ps/(nm2xc2x7km). Currently DC fibre is fabricated to a tolerance of xc2x13% in respect of linear dispersive power, and a tolerance of xc2x120% in respect of quadratic dispersive power. Therefore, for the 400 km span length, the uncertainty in linear dispersion compensation at the 1550 nm wavelength will amount to approximately 400 ps/nm (≈400xc3x9717xc3x970.06 ps/nm).
Given the 200 nm wavelength range, the additional uncertainty at the wavelength extremities produced by the xc2x120% quadratic tolerance amounts approximately to a further 900 ps/nm (≈400xc3x970.058xc3x97200xc3x970.2 ps/nm). To this must be added any uncertainty arising from any imprecision in the knowledge of the length and dispersion of the transmission fibre.
The foregoing indicates that, even if the DC fibre were manufactured to tolerances tightened by an order of magnitude, those tolerances would still be large enough to cause difficulty in achieving an accurate enough compensation for the reliable provision of an operating point near the centre of the 100 ps/nm window.
There is therefore a useful role for an adjustable amplitude linear dispersion compensation device. Such a device could be one designed for operation on its own to achieve the totality of dispersion compensation. Alternatively, it could be one designed for operation in association with a fixed amplitude dispersion compensation device, such as a length of DC fibre, that provides a level of compensation that is inadequately matched on its own. The adjustable device may be operated with some form of feedback control loop to provide active compensation that can respond to dynamic changes of dispersion within the system, and in suitable circumstances to step changes resulting from re-routing occasioned for instance by a partial failure of the system such as a transmission fibre break.
An alternative way of providing dispersion which may be used for dispersion compensation purposes utilises spectrally distributed reflection of light produced by a chirped Bragg grating extending in the axial direction of an optical waveguide. Such a method is for instance described in U.S. Pat. No. 4,953,939. Operating upon an optical waveguide with a Bragg reflective grating in such a way as to modify the pitch of its grating elements can have the effect of producing a change in the dispersion exhibited by that device, but in certain circumstances will not do so. Thus, if the starting point is a device with a uniform pitch Bragg grating, this device reflects light at the Bragg wavelength determined by that pitch, and the effect of the grating is not such as to impart any dispersion. If now the device is uniformly stretched, the magnitude of the pitch is changed, the Bragg reflection wavelength is changed, but the grating still does not impart any dispersion. A similar situation pertains if, instead of stretching the fibre to change the pitch of its grating elements, its effective pitch (the product of physical pitch with effective refractive index) is changed by a uniform heating of the grating. On the other hand, if the heating is not uniform, but is such as to produce a thermal gradient along the waveguide axis in the region of the grating, then the effect of this heating is to introduce chirp where none was present before, and hence is to introduce a measure of dispersion. Controlling the magnitude of the thermal gradient controls the magnitude of the resulting chirp, and thus there is provided a form of adjustable amplitude linear dispersion compensation device. Such a device is for instance described by B J Eggleton et al. in, xe2x80x98Dispersion compensation in 20 Gbit/s dynamic nonlinear lightwave systems using electrically tunable chirped fibre gratingxe2x80x99, Electronics Letters Vol. 35, No. 10, pp 832-3. Similarly, if the waveguide is subjected to a stretching that is not uniform, but is such as to produce a strain gradient along the waveguide axis, then the effect is to produce a controllable amplitude of chirp where none was present before. One example of such a device, a device in which a strain gradient is imparted to an optical fibre waveguide by bonding a portion of its length to a cantilever, and then bending that cantilever, is described by T Imai et al. in, xe2x80x98Dispersion Tuning of a Linearly Chirped Fiber Bragg Grating Without a Center Wavelength Shift by Applying a Strain Gradientxe2x80x99, IEEE Photonics Technology Letters, Vol. 10, No. 6, pp 845-7. Another example of such a device, a device in which a strain gradient is imparted to an optical fibre by bonding it to the side of a stack of electrostrictive elements, and then applying a differential drive to those elements, is described in U.S. Pat. No. 5,694,501. In the thermal and both strain based examples there is a liability to problems arising from the fact that any significant change of chirp is associated with a change in reflectivity. In the case of the thermal example there are the additional problems of slow response and of maintaining a controlled temperature gradient in a system environment as opposed to a controlled laboratory environment. In the case of the cantilever device, there are problems associated with the bonding of the fibre adequately to the cantilever, and extraneous optical non-linearities are introduced by virtue of the fact that the radius of curvature is typically a non-linear function of distance along the cantilever. In the case of the piezoelectric stack device, there are similar bonding problems, and there are cost and reliability problems associated with the complexity of the stack and the differential drive requirements of the component elements.
It has already been explained why the uniform stretching of an optical waveguide possessing a uniform pitch Bragg reflection grating does not introduce any change is linear dispersion. It can additionally be seen that uniform stretching similarly produces a negligible change in linear dispersion if the grating is linearly chirped. However, as for instance disclosed by K -M Feng et al. in, xe2x80x98Dynamic Dispersion in a 10-Gbit/s Optical System Using a Novel Voltage Tuned Nonlinearly Chirped Fiber Bragg Gratingxe2x80x99, IEEE Photonics Technology Letters, Vol. 11, No. 3, pp 373-5, the uniform stretching of an optical waveguide possessing a chirped Bragg grating with a quadratic component of its chirp does induce a change in the linear dispersion afforded by the structure.
The above-referenced paper by Feng et al. demonstrates, both in terms of eye diagram and BER measurement, how the use of their non-linearly chirped grating can be operated to reduce the receiver sensitivity penalty (increase in receiver signal power required to meet a given BER at 10 Gbit/s) of an uncompensated transmission system, and specifically attributes a residual receiver sensitivity penalty mainly to an imperfect compensation of the dispersion. We have determined that another factor is involved, namely that the presence of quadratic dispersion itself introduces a receiver sensitivity penalty.
It is for instance estimated that, in the case of a 40 Gbit/s NRZ system in which the quadratic dispersion amounts to only 40 ps/nm2, this penalty may amount to about 0.25 dB, and that the penalty increases in an approximately linear fashion with increasing quadratic dispersion, at least as far as a quadratic dispersion of 300 ps/nm2. This estimation is based on a simulation using a 128 bit Pseudo Random Bit Sequence generated with raised-cosine rising and falling edges. This is converted to an optical signal using the amplitude and phase response of a Mach-Zehnder modulator with symmetrical drive. The signal is then modified by the response of an optical fibre which can introduce quadratic dispersion across the modulation bandwidth. The resultant output from such a simulation is a pulse sequence, which is distorted in relation to the input pulse sequence. One way in which to assess the degradation is to overlay each received bit on top of its predecessors to generate an eye diagram. The actual method of assessing this eye diagram involves measuring quantitatively the amount of opening in the eye pattern. This figure is then compared to that of the system when there is no fibre in place. The ratio of these two figures is expressed in dB and quoted as a xe2x80x98penaltyxe2x80x99. The results of this estimation would prima facie suggest the choice of a grating with a low modulus quadratic chirp. However, for any given range of linear dispersion adjustment, a reduction in the modulus of quadratic chirp requires a corresponding increase in both grating length and the amount of strain required to sweep through that range. Good quality long Bragg reflection gratings are difficult to fabricate in optical waveguide because they are typically written in the guide sequentially section by section in short sections that need to be critically positioned with respect to each other to avoid excessive stitch error mediated quality degradation. Additionally, excessive strains are unwelcome because of associated problems of susceptibility to catastrophic failure by fracture.
Consider the general case of a structure for which the delay, expressed as a function of (free space) wavelength has only a zero offset, a linear component and a quadratic component, i.e. a structure that satisfies the relationship:
xcfx84(xcex)=a0+a1xcex+a2xcex2xe2x80x83xe2x80x83(1)
The linear dispersion is therefore given by:                               D          ⁡                      (            λ            )                          =                                            ⅆ              τ                                      ⅆ              λ                                =                                    a              1                        +                          2              ⁢                              a                2                            ⁢              λ                                                          (        2        )            
and the quadratic dispersion by:                               Q          ⁡                      (            λ            )                          =                                            ⅆ              D                                      ⅆ              λ                                =                                                                      ⅆ                  2                                ⁢                τ                                            ⅆ                                  λ                  2                                                      =                          2              ⁢                              a                2                                                                        (        3        )            
(Equation (3) shows that, because the differential group delay contains no cubic or higher order term, the quadratic dispersion, Q, is actually a constant, 2a2, rather than a term functionally dependent upon wavelength,xcex.) Equation (1) may with advantage be rewritten in terms of the zero offset delay xcfx840, the linear dispersion D0, and quadratic dispersion Q0 values (Q0=Q) pertaining to some chosen baseline wavelength xcex0. This baseline wavelength xcex0 is typically a wavelength at one end of (or in the middle of) the wavelength range over which dispersion compensation is required. Such a rewriting gives:                               τ          ⁢                      xe2x80x83                    ⁢                      (            λ            )                          =                              (                                          τ                0                            -                                                D                  0                                ⁢                                  λ                  0                                            +                                                                    Q                    0                                    2                                ·                                  λ                  0                  2                                                      )                    +                                    (                                                D                  0                                -                                                      Q                    0                                    ⁢                                      λ                    0                                                              )                        ⁢            λ                    +                                                    Q                0                            2                        ·                          λ              2                                                          (        4        )            
Under the assumption that the delay is produced by a non-linearly chirped Bragg grating in an optical waveguide with an effective refractive index n, each wavelength component xcex of the incident light is effectively reflected at some specific distance z(xcex) along the length of the grating. The delay xcfx84(xcex) is therefore the folded physical path length (2z) divided by the propagation speed of light in the waveguide (c/n), where c is the in vacuo speed of light.
Hence:                               τ          ⁡                      (            λ            )                          =                                            2              ⁢              n                        c                    ·                      z            ⁡                          (              λ              )                                                          (        5        )            
Substituting equation (5) in equation (4) together with:
xcex94xcex=xcexxe2x88x92xcex0xe2x80x83xe2x80x83(6)
gives:                               τ          ⁡                      (            λ            )                          =                                                            2                ⁢                n                            c                        ·                          z              ⁡                              (                λ                )                                              =                                    τ              0                        +                                                            D                  0                                ·                Δ                            ⁢                              xe2x80x83                            ⁢              λ                        +                                                                                Q                    0                                    2                                ·                Δ                            ⁢                              xe2x80x83                            ⁢                              λ                2                                                                        (        7        )            
Equation (7) is a quadratic equation in xcex94xcex whose solution, under the condition that z=0 at xcfx840=0, is given by:                               Δ          ⁢                      xe2x80x83                    ⁢          λ                ⁢                  xe2x80x83                =                                            -                              D                0                                      ±                                                            D                  0                  2                                +                                                                            4                      ⁢                                              Q                        0                                            ⁢                      n                                        c                                    ·                  z                                                                          Q            0                                              (        8        )            
Remembering that the physical pitch, xcex9, of the grating, is related to the Bragg wavelength xcex by:
xcex=2nxc2x7xcex9xe2x80x83xe2x80x83(9)
equation (8) also provides a description of the pitch variation of the grating.
Differentiating equation (7) with respect to xcex, and rearranging, gives:
D(xcex)=D0+Q0xc2x7xcex94xcexxe2x80x83xe2x80x83(10)
Accordingly, a linear dispersion range xcex94D=D1xe2x88x92D0 requires a bandwidth:                     B        =                                            λ              1                        -                          λ              0                                =                                    Δ              ⁢                              xe2x80x83                            ⁢              D                                      Q              0                                                          (        11        )            
Substituting equation (11) in equation (7) to find the granting length, xcex94z, gives:                               Δ          ⁢                      xe2x80x83                    ⁢          z                =                              c                          4              ⁢              n              ⁢                              xe2x80x83                            ⁢                              Q                0                                              ⁢                      (                                          2                ⁢                                                      D                    0                                    ·                  Δ                                ⁢                                  xe2x80x83                                ⁢                D                            +                              Δ                ⁢                                  xe2x80x83                                ⁢                                  D                  2                                                      )                                              (        12        )            
Equation (12) defines the length of a grating that is required to meet a given design specification. For instance, assuming n=1.5, and that a linear dispersion range from D0=100 ps/km to D1=500 ps/km is required with a quadratic dispersion mediated receiver sensitivity penalty limited by limiting the quadratic dispersion to Q0=20 ps/km2; equation (12) determines that the grating must be 600 mm long. For many application this is inconveniently long, and moreover would involve excessive stretching to cover the full range (a strain range of approximately 1.2% for operation in the wavelength region of 1550 nm). Increasing the quadratic dispersion limit by a factor of ten to Q0=200 ps/km2 reduces the grating length, and the strain range, each by a factor of ten, but only achieves this at the expense of a significant increase in receiver sensitivity penalty.
An object of the present invention is to provide a way of cancelling, at least in part, the receiver sensitivity penalty of an adjustable linear dispersion compensator that employs a waveguide provided with chirped Bragg reflection grating that has a quadratic component of chirp.
According to a first aspect of the present invention, there is provided a method of providing adjustable linear dispersion by causing light to make first and second spectrally distributed reflections respectively in first and second optical waveguides provided with associated first and second chirped Bragg grating reflectors having quadratic components of chirp of opposite sign and substantially matched modulus, each Bragg grating reflector having an effective pitch which is a function of position along that Bragg grating reflector, and which is the product of its physical pitch at that position with the effective refractive index of the waveguide associated with that Bragg grating reflector, in which method an adjustment of linear dispersion is provided by a differential scaling of the effective pitches of the two Bragg grating reflectors.
Since physical pitch and waveguide effective refractive index both contribute to the effective pitch of a Bragg grating reflector, a scaling of its effective pitch, a multiplication by some numerical factor not equal to 1, is achievable by either of these parameters, or of both parameters in combination, a scaling of the effective pitch, resulting at least predominately from a scaling of the physical pitch is obtainable by the application of stress to produce axial strain in the fibre, typically tensile strain. On the other hand, in the case of a polymer optical waveguide (which may be, but is not necessarily, a polymer optical fibre waveguide) a scaling of the effective pitch, resulting at least predominately from a scaling of the effective refractive index of the waveguide is obtainable by changing its temperature. In this instance use is being made of the fact that the temperature coefficient of polymer optical waveguide (dn/dT) is generally much larger than that of silica waveguide.
In the case of a Bragg reflective grating formed in a silica optical fibre waveguide, such a waveguide may be a standard silica fibre waveguide, or it may be a silica fibre waveguide of a composition providing enhanced photosensitivity.
According to a second aspect of the present invention, there is provided a method of providing adjustable linear dispersion by causing light to make first and second spectrally distributed reflections respectively in first and second optical waveguides provided with associated first and second differentially strainable chirped Bragg grating reflectors having quadratic components of chirp of opposite sign and substantially matched modulus. device exhibiting linear dispersion of adjustable magnitude, which device includes first and second optical waveguides provided with respective first and second chirped Bragg reflection gratings and is arranged to define an optical transmission path that includes a reflection in both gratings, wherein the first waveguide is mechanically coupled with a strain applicator adapted to impart to the first waveguide, over the length of its Bragg grating, a substantially uniform axial strain of adjustable magnitude, and wherein the first and second gratings have quadratic components of chirp of opposite sign and substantially matched modulus.
According to a fourth aspect of the present invention, there is provided a device exhibiting linear dispersion of adjustable magnitude, which device includes first and second optical waveguides provided with respective first and second chirped Bragg reflection gratings and is arranged to define an optical transmission path that includes a reflection in both gratings, and also includes a thermal regulator adapted to maintain a uniform temperature difference between said first and second chirped Bragg reflection gratings of adjustable magnitude, and wherein the first and second gratings have quadratic components of chirp of opposite sign and substantially matched modulus.
Other features and advantages of the invention will be readily apparent from the following description of preferred embodiments of the invention, from the drawings and from the claims.